Biomechanical simulation for cartilage regeneration of knee joint osteoarthritis with composite scaffold using ply angle optimization

Abstract

This study investigates the optimization of the ply angle for cartilage regeneration using a composite scaffold for treating knee joint osteoarthritis. We propose a new paradigm for composite scaffold tissue engineering that focuses on the reconstitution of the anatomic fiber architecture and uses constitutive modeling to evaluate the function of the construct. The mechano-regulation algorithm for tissue differentiation was used to determine the influence of the composite scaffold with an optimized ply angle on chondrogenesis in a computational model of knee-joint severe osteoarthritis. The simulation results revealed that the optimized ply-angle composite scaffold, which had similar mechanical properties to the native cartilage, provided the most appropriate biomechanical environment for cartilage regeneration.

Keywords

Scaffold composite finite element method cartilage knee

Introduction

Articular cartilage is a remarkably strong tissue capable of enduring significant loads over time but has a limited healing capacity owing to its avascular nature.^1,2 In particular, damage to focal cartilage occurs frequently in the knee joint and does not heal quickly.³ Patients with focal cartilage damage often suffer from pain and functional impairment, which significantly affect their quality of life.⁴ Additionally, cartilage defects that do not involve the subchondral bone have limited to no spontaneous repair potential and can result in symptoms equivalent to those observed in severe osteoarthritis (OA).^5,6 OA is a degenerative disease involving the entire joint, including the articular cartilage, subchondral bone, and periarticular tissue. The poor intrinsic healing potential of damaged cartilage, which results in progressive degradation of articular cartilage and subsequent widespread degeneration of the joint, is a major clinical problem in OA treatment.^7,8 Therefore, various methods have been introduced for the surgical treatment of cartilage lesions, including microfracture and restorative techniques, such as osteochondral autograft transfer, mosaicplasty, and frozen osteochondral allografts, which were developed to transfer articular hyaline cartilage into the injured area.^9–11 However, the outcomes of these procedures are often unfavorable because of the biomechanical insufficiency of the regenerative fibrocartilage compared with the hyaline cartilage. Therefore, the effectiveness of these procedures in treating OA knees is debatable. Nevertheless, although the precise mechanism whereby these procedures improve the course of degenerative conditions of the knee has not been identified, cartilage regenerative procedures have become the focus of increased interest because of their potential to provide pain relief and alter the progression of OA. Recently, mesenchymal stem cells (MSCs) and chondrocytes have been suggested for use in the cell-based treatment of cartilage lesions. In particular, MSCs exhibit significant potential as therapeutic agents in regenerative medicine because of their multilineage potential, immunosuppressive activity, limited immunogenicity, and relative ease of growth in culture.¹² The direct intra-articular injection of MSCs into an OA knee has been performed and is the most commonly used method for OA treatment.^13,14 However, a simple injection is insufficient for achieving improved cell engraftment, because directly injected cells have limited cell retention and survival at the target site. It is becoming apparent that, without support from an intact subchondral bed, any treatment of the surface chondral lesion is more likely to fail.¹⁵ These intralesional osteophytes are recommended to be removed during revision with autologous chondrocyte implantation and MSCs to thin out the thickened subchondral plate, to mechanically reduce the pathologically elevated stiffness and to simply create space in the defect for the regenerative tissue.¹⁶ Therefore, tissue-engineered scaffolds may be needed to treat patients with large cartilage lesions. Additionally, the scaffold is simultaneously degraded by the body and reinforced by the generation of new tissue. Previously, a mechano-regulation model was developed to relate the differentiation of cells of the mesenchymal lineage to their mechanical environment, and it was used to successfully predict the patterns of tissue differentiation during cartilage regeneration.^17,18 A finite element (FE) model offers the possibility of investigating the behavior of tissues and scaffolds, such as cartilage regeneration status in complex structures, for determining the mechanical and clinical requirements of scaffolds.¹⁹

Kelly and Prendergast mechano-regulation theory for tissue differentiation was used to evaluate the influence of scaffold material properties on chondrogenesis using an FE model of an osteochondral defect.¹⁷ Recently, Koh et al. predicted the mechanical properties of an optimum scaffold for cartilage regeneration using computational simulation with medical imaging and mechano-regulation theory under stance phase gait cycle loading conditions.²⁰ Different types of mechano-regulation theories have been developed for the estimation of regeneration process.^21–23 These theories include different mechanical stimuli, including interfragmentary strain, deviatoric strain, hydrostatic pressure, fluid velocity, and principal strain.^21,23,24 Previously, we used mechano-regulation algorithms such as deviatoric strain and fluid flow were used in FE analysis to predict the cartilage regeneration process more accurately stance phase gait cycle loading conditions.^24,25 Recent studies showed fiber-reinforced composite scaffold (CS) that can capture the zonal depth-dependent mechanical properties of native cartilage, and simultaneously support neo-cartilage formation.^26,27 Theoretically, the mechanical properties of a CS also affect the cartilage regeneration. The design parameters including the average Young’s modulus, degradation rate of material, and the ply angle of the CS are the major parameters that should be optimally selected.

Therefore, the most effective ply angle of a laminated CS membrane for cartilage regeneration was evaluated using the mechano-regulation algorithm and an optimization method in this study. We developed a biphasic poroelastic FE model that mimics the solid and liquid phases of actual damage conditions, and determined the regeneration process of cartilage defects using the mechano-regulation theory. Regarding the mechanical environment, the effects of an optimized ply-angle CS on the cartilage regeneration process were investigated. We hypothesized that an optimized ply-angle laminated composite scaffold membrane (LCSM) is the most efficient alternative for cartilage regeneration.

Materials and methods

Knee joint modeling

An existing three-dimensional (3D) knee joint model was used to develop a cartilage regeneration FE model^28–30 (Figure 1). An FE model of the lower extremities was developed using imaging data obtained from a healthy and skeletally mature young male athlete without any history of knee injury. A 3D nonlinear FE model of a normal knee joint was developed using data obtained from computed tomography (CT) and magnetic resonance imaging (MRI) scans of a healthy 37-year-old male subject. The CT and MRI images were developed with slice thicknesses of 0.1 and 0.4 mm, and were used to develop bony structures and soft tissues, respectively. The MRI was used to reconstruct a femur with a distal thickness of 10.2 cm and a tibia with a proximal thickness of 7 cm. To match the positional coordinates of each model, anatomic reference points were used as the central point of the diaphysis of the femur, the midpoint of the transepicondylar axis, and the intercondylar notch in the reconstructed CT and MRI models.³¹ The reconstructed CT and MRI models were combined with a positional alignment of each model by using commercial software (Rapidform version 2006; 3D Systems Korea Inc., Seoul, South Korea). The initial graphics exchange specification (IGES) files exported from Mimics were entered into Unigraphics NX (version 7.0; Siemens PLM Software, Torrance, CA) to develop solid models for each femur, tibia, fibula, patella, and soft-tissue segment. The solid model was then imported into Hypermesh (version 8.0; Altair Engineering, Troy, MI) to generate an FE mesh followed by analyzing with ABAQUS software (version 6.11; Simulia, Providence, RI). A poroelastic element (C3D8RP) with a mesh size of 1 mm was used for the calluses to ensure the accuracy of convergence. Contact was modeled between the femoral cartilage and meniscus, meniscus and tibial cartilage, and femoral cartilage and tibial cartilage for both medial and lateral sides, and this resulted in six contact pairs. Thus, the components were not penetrating. More details of overall procedure are shown in Figure 1.

Mechano-regulation algorithm

Mechano-regulation algorithm processes are driven by the mechanical environment of a cell. Computational techniques such as FE modeling facilitate the calculation of the mechanical stimuli within the extracellular matrix of a regenerating tissue. In this study, cartilage defects within the knee were analyzed using an FE model. The mechano-regulation theory was implemented in each element of the cartilage regeneration.¹⁸ Calluses were initially filled with granulation tissue and were surrounded by mesenchymal cells. The calluses were considered to be soil-like materials to mimic the solids and fluid in pores. Fluid can flow in all elements within the pores of calluses; however, the outer layers of calluses were considered to be impermeable. To simulate the diffusion of stem cells throughout the calluses, a diffusion coefficient was chosen to predict stem cell coverage of 99% six weeks after surgery.¹⁸

The differentiation of the granulation tissue in a given element into fibrous tissue, cartilage, or bone was subsequently determined by the following stimulus factor (S)

S = γ / a + v / b

(1)

where γ represents the octahedral shear strain; ν represents the fluid velocity; a (3.75%) and b (3 µm/s) are the scaling factors for each stimulus. According to the mechano-regulation theory, S > 3 indicates fibrous connective tissue, 1 < S < 3 indicates cartilage, 0.53 < S < 1 indicates immature woven bone, 0.01 < S < 0.53 indicates mature woven bone, and 0 < S < 0.01 indicates bone resorption.^17,18,32,33

The poroelastic material properties were updated according to a rule of mixtures based on the concentration of cells in a given element (n_c) and the volume fractions (φj) and material properties of the granulation tissue and j types of differentiated tissues in the element. For example, the Young’s modulus (E) for a given element was calculated as follows

E = \frac{(n_{c}^{\max} - n_{c})}{n_{c}^{\max}} E_{granulation} + \frac{n_{c}}{n_{c}^{\max}} \sum_{j = 1}^{n_{t}} E_{j} φ_{j}

(2)

where

n_{c}^{\max}

represents the maximum number of cells that can occupy any single element, and E_j represents the Young’s modulus of the jth differentiated tissue. The volume fraction φ_j of a given type of differentiated tissue was evaluated as the fraction of the last 10 iterations wherein the differentiated tissue type was predicted in the element. This enabled the material properties to change gradually, preventing instability in the algorithm.³³ Each material property was calculated for each element with the formula by using a custom FORTRAN script. Each of these cellular events was implemented into an algorithm, and a graphical summary is shown in Figure 2. The material properties of the living tissues are presented in Table 1.^32–34

Table 1.

The material properties used for each tissue type. Young’s modulus (MPa).^32–34

	Young’s modulus (MPa)	Poisson’s ratio
Cartilage	15	0.47
Meniscus	120 (circumferential direction)	0.20 (circumferential and radial direction)
Meniscus	20 (axial and radial direction)	0.30 (axial direction)

Homogenization modeling of LCSM

An established two-dimensional (2D) homogenization model for linear elastic fiber-reinforced soft tissues was adapted to characterize the mechanical behavior of poly-e-caprolactone (PCL) fiber-aligned scaffolds.³⁵ Homogenization is a method whereby composite materials are characterized by mathematically averaging the heterogeneous material properties of the constituents: a “fiber” component embedded in a “matrix.” Such a model allows for the determination of a homogenized (e.g., averaged) elasticity tensor, C, and thereby the homogenized composite modulus, using five inputs: the fiber volume fraction (r), matrix modulus (E_m), matrix Poisson’s ratio (nm), fiber modulus (E_f), and fiber Poisson’s ratio (n_f). The material used to prepare the membrane was a PCL fiber composite. To obtain the properties of the 2D homogenization model, we used a composite formula available in the literature.^36,37 Assuming a plane stress condition, we have defined the stress–strain relationship as follows

[\begin{matrix} σ_{1} \\ σ_{2} \\ τ_{6} \end{matrix}] = [\begin{matrix} Q_{11} & Q_{12} & 0 \\ Q_{12} & Q_{22} & 0 \\ 0 & 0 & Q_{66} \end{matrix}] [\begin{matrix} ε_{1} \\ ε_{2} \\ γ_{6} \end{matrix}]

Using the homogenization model, the [Q] component was obtained as follows

\begin{array}{l} Q_{11} = \frac{ρ E_{f}}{1 - ν_{f}^{2}} + \frac{(1 - ρ) E_{m}}{1 - ν_{m}^{2}} - \frac{ρ E_{f} ν_{f}^{2}}{1 - ν_{f}^{2}} - \frac{(1 - ρ) E_{m} ν_{m}^{2}}{1 - ν_{m}^{2}} \\ + \frac{{(ρ ν_{f} + (1 - ρ) ν_{m})}^{2} E_{m} E_{f}}{ρ E_{m} (1 - ν_{f}^{2}) + (1 - ρ) (1 - ν_{m}^{2}) E_{f}} \\ Q_{12} = \frac{(ρ ν_{f} + (1 - ρ) ν_{m}) E_{m} E_{f}}{ρ E_{m} (1 - ν_{f}^{2}) + (1 - ρ) (1 - ν_{m}^{2}) E_{f}} \\ Q_{22} = \frac{E_{m} E_{f}}{ρ E_{m} (1 - ν_{f}^{2}) + (1 - ρ) (1 - ν_{m}^{2}) E_{f}} \\ Q_{66} = \frac{1}{2} \frac{E_{m} E_{f}}{ρ E_{m} (1 - ν_{f}) + (1 - ρ) (1 + ν_{m}) E_{f}} \end{array}

The modulus and Poisson’s ratio of the PCL fiber (E_f, ν_f) were 120 MPa and 0.49, respectively. The modulus and Poisson’s ratio of the matrix (E_m, ν_m) were 1 MPa and 0.25, respectively. The fiber volume ratio, ρ, was 0.15. The inverse matrix [S] of [Q] was obtained and used to calculate the engineering constant as follows

{[\begin{array}{c} Q_{11} & Q_{12} & 0 \\ Q_{12} & Q_{22} & 0 \\ 0 & 0 & Q_{66} \end{array}]}^{- 1} = [\begin{array}{c} S_{11} & S_{12} & 0 \\ S_{12} & S_{22} & 0 \\ 0 & 0 & S_{66} \end{array}]

S_{11} = \frac{1}{E_{1}} S_{22} = \frac{1}{E_{2}} S_{12} = S_{21} = - \frac{ν_{12}}{E_{1}} = - \frac{ν_{21}}{E_{2}} S_{66} = \frac{1}{G_{12}}

The calculated engineering constants were as follows: E₁ = 18.85 MPa, E₂ = E₃ = 1.25 MPa, ν₁₂ = ν₁₃ = 0.286, G₁₂ = G₁₃ = 0.47 MPa. Using a self-consistent field model,³⁶ the out-of-plane material properties were calculated as follows: ν₂₃ = 0.326, G₂₃ = 0.5 MPa.

Optimization and loading conditions

We optimized the ply angle of the LCSM to determine the best cartilage regeneration condition. The structural performance of the LCSM is susceptible to changes in the angles of the fiber orientations of the plies. The ply angle was optimized via division with a discrete value of 15°. The material properties of the scaffold and the ply angle were optimized using Isight (version 5.9; Dassault Systèmes). The optimization was performed by using the non-dominated sorting genetic algorithm (NSGA2), which was introduced in a previous study as an appropriate method for solving multi-objective problems.^38,39 The optimization was performed to determine the material properties and ply angle that yields the optimal regeneration of cartilage. The loading condition was a stance-phase gait cycle from the ISO 14243–1 standard (Figure 2).⁴⁰ All FE analyses were conducted using ABAQUS 6.11 (Simulia, Providence, RI, USA).

Results

Figure 4 shows the conditions of no scaffold, a [0]₁₂ LCSM, and the optimized-ply-angle LCSM for tissue differentiation in cartilage defects during the gait cycle loading. High and low levels of stimulus differentiate the mesenchymal cells into fibroblasts and osteoblasts, respectively. However, moderate levels of stimulus differentiate the chondrocytes. In the no-scaffold simulation condition, the defect was partially shielded from the load by the adjacent intact cartilage, and the stimulus within the defect was low. This low level of mechanical stimulus favors osteogenesis. As the repair tissue starts to stiffen, it supports the load, and chondrogenesis is favored within the defect center. Fibrous tissue is predicted to form at the articular surface owing to the high magnitudes of strain and fluid flow in repairing the tissue region (Figure 4). Regions of cartilage start to differentiate into fibrous tissue, reducing the amount of cartilage within the defect (Figure 4). However, with the optimized ply angle of the LCSM, the formation of cartilage tissue is primarily predicted in the chondral region of the defect. The optimized ply angle of the LCSM is predicted to support early chondrogenesis, with the chondral region of the defect primarily having immature cartilage tissue. Increased cartilage formation is predicted in the simulation of defect regeneration, with a greater proportion of the defect having cartilage tissue. A uniform band of fibrous tissue persists at the articular surface; however, the remainder of the chondral part of the defect is nearly exclusively made of cartilage tissue. For the [0]₁₂ LCSM, fibrous tissue is predicted to form at the articular surface in the regeneration tissue region, although in a smaller amount compared with the no-scaffold condition (Figure 4). During the regeneration in the no-scaffold case, significant cell death is predicted at the articular surface owing to the high stimulus (Figure 5). Implanting an optimized ply-angle LCSM is expected to prevent cell death owing to the lower stimulus experienced by the cells in the presence of the scaffold (Figure 5). For the [0]₁₂ LCSM, fibrous tissue is predicted to form at the articular surface in the regeneration tissue region, although in a smaller amount compared with the no-scaffold condition (Figure 5). Figure 6 shows the quantification of the tissue differentiation during iteration. The immature cartilage with no scaffold increased slightly for 10 iterations; however, the fibrous tissue rapidly increased in 40 iterations with a sudden reduction in the mature cartilage tissue (Figure 6). Nonetheless, improved regeneration was observed when the optimized ply-angle LCSM was used. A continuous increase in the immature cartilage from the first iteration was observed with a jump after 40 iterations, owing to the proper cartilage regeneration. Table 2 presents the optimum ply angle of the LCSM.

Table 2.

The optimum ply angle of LCSM.

Ply sequence	Ply angle (degree)
1	0
2	90
3	15
4	−75
5	75
6	−15
7	−15
8	75
9	−75
10	15
11	90
12	0

Discussion

The most important finding of this study is that the optimum ply-angle LCSM was more effective at cartilage regeneration than the [0]₁₂ LCSM and the use of no scaffold.

OA is the most prevalent chronic disease owing to the degeneration of the articular cartilage and it is accompanied by subchondral bone sclerosis and synovial inflammation.⁴¹ Restoration of the diseased articular cartilage in patients with OA is a difficult problem for researchers and clinicians.⁴² As a potential cell-based therapy for cartilage repair, MSCs have been suggested for the treatment of diseased articular cartilage, and a few studies on the clinical use of MSCs for OA have been published.^13,14,43 Additionally, direct intra-articular injection of MSCs into an OA knee has been considered in several studies.^13,14,44

However, simple injection is insufficient for achieving improved cell engraftment, because directly injected cells have limited cell retention and survival at the target site.⁴⁵ In our previous study, we performed MSC implantation under arthroscopic guidance according to the local adherent technique to further optimize implantation and prevent cell loss, which was reported by Koh et al.⁴⁵ Koga et al.⁴⁶ However, large cartilage lesions exhibited worse outcomes, and we concluded that the development of an advanced surgical procedure with tissue-engineered scaffolds is needed to treat patients with large cartilage lesions.⁴⁷

Therefore, the ideal scaffold should be biocompatible and biodegradable upon tissue healing; highly porous to allow cell penetration and tissue impregnation, to permit nutrient delivery and gas exchange; and adaptable to the mechanical environment. Diverse biomaterials are used as scaffolds to deliver MSCs for cartilage repair, but they do not satisfy all the aforementioned requirements.⁴⁸ In a fiber-reinforced orthopedic scaffold, special consideration should be given to the underlying unique features that dictate the mechanical behavior of the native tissue. One challenge regarding the native collagen fiber of articular cartilage is that the direction of the maximum applied stress is not parallel to the predominant fiber direction of the tissue. In a previous study, it was shown that the PCL scaffold mimics both the anisotropy and nonlinearity of the basic functional unit of the collagen fiber, i.e., the single fiber-aligned lamella.³⁷ Further, it was shown that the orientation of fiber-aligned scaffolds with respect to the prevailing fiber direction generates vastly different mechanical behaviors, and the ability to predict this phenomenon using a model applied to native collagen fiber tissue was demonstrated.³⁷ Therefore, we converted the PCL scaffold material into a 3D homogenization model. In this study, the optimal ply angle of the LCSM for achieving successful cartilage regeneration was investigated. The result indicates that the Young’s modulus of a scaffold should be similar to that of the native cartilage and that an appropriate modulus of a scaffold should be selected to achieve sufficient mechanical stability. The results suggest the potential of the proposed ply-angle optimization scheme to allow the design of material with unusual properties or to achieve the prescribed elasticity. When the optimum ply-angle scaffold is employed for cartilage tissue engineering, it can match the properties of the native cartilage tissue, with a stiffness ranging from 5 to 50 MPa, covering the range of stiffnesses from biopolymer to bio-ceramic.

The ability to closely match the target cartilage properties depends on the chosen base material stiffness. For example, if the target stiffness is 10 MPa and the base material stiffness is 20 GPa, it is impossible to match the target stiffness with an optimized ply angle.

Additionally, in a previous study bone formation through both endochondral and direct intramembranous ossification in a defect, cartilage formation in the center of the defect, and fibrous tissue formation were observed.⁴⁹ This regeneration pattern was also observed in our FE model.

If improved regeneration is defined as maximizing the cartilage tissue formed in the chondral part of the defect, which minimizes the formation of fibrous tissue, produces a uniformly thick layer of cartilage repair tissue, and prevents cell death within the defect, it is suggested that a scaffold must have a certain minimum stiffness to reduce the formation of fibrous tissue within the defect.¹⁷ However, if the scaffold is excessively stiff, the amount of fibrous tissue predicted to form within the defect begins to increase (Figures 4 and 6) because of an increase in the magnitude of fluid flow within the defect. Increasing the stiffness of the scaffold also reduces the repair cartilage thickness owing to the further progression of the osseous front. A similar trend was observed in a clinical study. Although the ply angle was not optimized, Gille et al. obtained promising results through the fiber membrane scaffold procedure for the treatment of focal cartilage defects of the knee.⁵⁰ Clinical evaluation for up to 60 months after implantation revealed an improvement of the patient’s condition with reliable clinical outcome scores and articular resurfacing as assessed using MRI. This supports our result that the fiber membrane scaffold is more effective in cartilage regeneration than the use of no scaffold.

Conclusions

It is concluded that the most influential design parameter is the ply angle of the CS. The genetic-algorithm method is very useful for optimizing the ply angle to achieve desirable results. To achieve an optimal porosity of prostheses for cartilage defects, various combinations of stiffnesses should be obtained using different ply angles of scaffolds along with material selection, which is yet to be investigated; this topic will be addressed in a future study.

Footnotes

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) received no financial support for the research, authorship, and/or publication of this article.

ORCID iD

Kyoung-Tak Kang

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